{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# VQE with Qiskit Aer Primitives\n",
    "\n",
    "This notebook demonstrates how to leverage the [Qiskit Aer Primitives](https://qiskit.org/ecosystem/aer/apidocs/aer_primitives.html) to run both noiseless and noisy simulations locally. Qiskit Aer not only allows you to define your own custom noise model, but also to easily create a noise model based on the properties of a real quantum device. This notebook will show an example of the latter, to illustrate the general workflow of running algorithms with local noisy simulators.\n",
    "\n",
    "For further information on the Qiskit Aer noise model, you can consult the [Qiskit Aer documentation](https://qiskit.org/ecosystem/aer/apidocs/aer_noise.html), as well the tutorial for [building noise models](https://qiskit.org/ecosystem/aer/tutorials/3_building_noise_models.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm of choice is once again VQE, where the task consists on finding the minimum (ground state) energy of a Hamiltonian. As shown in previous tutorials, VQE takes in a qubit operator as input. Here, you will take a set of Pauli operators that were originally computed by Qiskit Nature for the H2 molecule, using the [SparsePauliOp](https://qiskit.org/documentation/stubs/qiskit.quantum_info.SparsePauliOp.html#sparsepauliop) class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits: 2\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "H2_op = SparsePauliOp.from_list(\n",
    "    [\n",
    "        (\"II\", -1.052373245772859),\n",
    "        (\"IZ\", 0.39793742484318045),\n",
    "        (\"ZI\", -0.39793742484318045),\n",
    "        (\"ZZ\", -0.01128010425623538),\n",
    "        (\"XX\", 0.18093119978423156),\n",
    "    ]\n",
    ")\n",
    "\n",
    "print(f\"Number of qubits: {H2_op.num_qubits}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the above problem is still easily tractable classically, you can use `NumPyMinimumEigensolver` to compute a reference value to compare the results later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value: -1.85728\n"
     ]
    }
   ],
   "source": [
    "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n",
    "from qiskit.opflow import PauliSumOp\n",
    "\n",
    "numpy_solver = NumPyMinimumEigensolver()\n",
    "result = numpy_solver.compute_minimum_eigenvalue(operator=PauliSumOp(H2_op))\n",
    "ref_value = result.eigenvalue.real\n",
    "print(f\"Reference value: {ref_value:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following examples will all use the same ansatz and optimizer, defined as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define ansatz and optimizer\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit.algorithms.optimizers import SPSA\n",
    "\n",
    "iterations = 125\n",
    "ansatz = TwoLocal(rotation_blocks=\"ry\", entanglement_blocks=\"cz\")\n",
    "spsa = SPSA(maxiter=iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance *without* noise\n",
    "\n",
    "Let's first run the `VQE` on the default Aer simulator without adding noise, with a fixed seed for the run and transpilation to obtain reproducible results. This result should be relatively close to the reference value from the exact computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define callback\n",
    "# note: Re-run this cell to restart lists before training\n",
    "counts = []\n",
    "values = []\n",
    "\n",
    "\n",
    "def store_intermediate_result(eval_count, parameters, mean, std):\n",
    "    counts.append(eval_count)\n",
    "    values.append(mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define Aer Estimator for noiseless statevector simulation\n",
    "from qiskit.utils import algorithm_globals\n",
    "from qiskit_aer.primitives import Estimator as AerEstimator\n",
    "\n",
    "seed = 170\n",
    "algorithm_globals.random_seed = seed\n",
    "\n",
    "noiseless_estimator = AerEstimator(\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VQE on Aer qasm simulator (no noise): -1.84322\n",
      "Delta from reference energy value is 0.01406\n"
     ]
    }
   ],
   "source": [
    "# instantiate and run VQE\n",
    "from qiskit.algorithms.minimum_eigensolvers import VQE\n",
    "\n",
    "vqe = VQE(\n",
    "    noiseless_estimator, ansatz, optimizer=spsa, callback=store_intermediate_result\n",
    ")\n",
    "result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n",
    "\n",
    "print(f\"VQE on Aer qasm simulator (no noise): {result.eigenvalue.real:.5f}\")\n",
    "print(\n",
    "    f\"Delta from reference energy value is {(result.eigenvalue.real - ref_value):.5f}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You captured the energy values above during the convergence, so you can track the process in the graph below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Convergence with no noise')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "\n",
    "pylab.rcParams[\"figure.figsize\"] = (12, 4)\n",
    "pylab.plot(counts, values)\n",
    "pylab.xlabel(\"Eval count\")\n",
    "pylab.ylabel(\"Energy\")\n",
    "pylab.title(\"Convergence with no noise\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance *with* noise\n",
    "\n",
    "Now, let's add noise to our simulation. In particular, you will extract a noise model from a (fake) device. As stated in the introduction, it is also possible to create custom noise models from scratch, but this task is beyond the scope of this notebook.\n",
    "\n",
    "First, you need to get an actual device backend and from its `configuration` and `properties` you can setup a coupling map and a noise model to match the device. Note: You can also use this coupling map as the entanglement map for the variational form if you choose to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NoiseModel:\n",
      "  Basis gates: ['cx', 'id', 'rz', 'sx', 'x']\n",
      "  Instructions with noise: ['cx', 'sx', 'id', 'measure', 'x']\n",
      "  Qubits with noise: [0, 1, 2, 3, 4]\n",
      "  Specific qubit errors: [('id', (0,)), ('id', (1,)), ('id', (2,)), ('id', (3,)), ('id', (4,)), ('sx', (0,)), ('sx', (1,)), ('sx', (2,)), ('sx', (3,)), ('sx', (4,)), ('x', (0,)), ('x', (1,)), ('x', (2,)), ('x', (3,)), ('x', (4,)), ('cx', (3, 4)), ('cx', (4, 3)), ('cx', (3, 1)), ('cx', (1, 3)), ('cx', (1, 2)), ('cx', (2, 1)), ('cx', (0, 1)), ('cx', (1, 0)), ('measure', (0,)), ('measure', (1,)), ('measure', (2,)), ('measure', (3,)), ('measure', (4,))]\n"
     ]
    }
   ],
   "source": [
    "from qiskit_aer.noise import NoiseModel\n",
    "from qiskit.providers.fake_provider import FakeVigo\n",
    "\n",
    "# fake providers contain data from real IBM Quantum devices stored in Qiskit Terra,\n",
    "# and are useful for extracting realistic noise models.\n",
    "device = FakeVigo()\n",
    "\n",
    "coupling_map = device.configuration().coupling_map\n",
    "noise_model = NoiseModel.from_backend(device)\n",
    "\n",
    "print(noise_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the noise model is defined, you can run `VQE` using an Aer `Estimator`, where you can pass the noise model to the underlying simulator using the `backend_options` dictionary. Please note that this simulation will take longer than the noiseless one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "noisy_estimator = AerEstimator(\n",
    "    backend_options={\n",
    "        \"method\": \"density_matrix\",\n",
    "        \"coupling_map\": coupling_map,\n",
    "        \"noise_model\": noise_model,\n",
    "    },\n",
    "    run_options={\"seed\": seed, \"shots\": 1024},\n",
    "    transpile_options={\"seed_transpiler\": seed},\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of defining a new instance of the `VQE` class, you can now simply assign a new estimator to our previous `VQE` instance. As the callback method will be re-used, you will also need to re-start the `counts` and `values` variables to be able to plot the convergence graph later on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# re-start callback variables\n",
    "counts = []\n",
    "values = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VQE on Aer qasm simulator (with noise): -1.74645\n",
      "Delta from reference energy value is 0.11083\n"
     ]
    }
   ],
   "source": [
    "vqe.estimator = noisy_estimator\n",
    "\n",
    "result1 = vqe.compute_minimum_eigenvalue(operator=H2_op)\n",
    "\n",
    "print(f\"VQE on Aer qasm simulator (with noise): {result1.eigenvalue.real:.5f}\")\n",
    "print(\n",
    "    f\"Delta from reference energy value is {(result1.eigenvalue.real - ref_value):.5f}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if counts or values:\n",
    "    pylab.rcParams[\"figure.figsize\"] = (12, 4)\n",
    "    pylab.plot(counts, values)\n",
    "    pylab.xlabel(\"Eval count\")\n",
    "    pylab.ylabel(\"Energy\")\n",
    "    pylab.title(\"Convergence with noise\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, you compared three calculations for the H2 molecule ground state.  First, you produced a reference value using a classical minimum eigensolver. Then, you proceeded to run `VQE` using the Qiskit Aer `Estimator` with 1024 shots. Finally, you extracted a noise model from a backend and used it to define a new `Estimator` for noisy simulations. The results are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value: -1.85728\n",
      "VQE on Aer qasm simulator (no noise): -1.84322\n",
      "VQE on Aer qasm simulator (with noise): -1.74645\n"
     ]
    }
   ],
   "source": [
    "print(f\"Reference value: {ref_value:.5f}\")\n",
    "print(f\"VQE on Aer qasm simulator (no noise): {result.eigenvalue.real:.5f}\")\n",
    "print(f\"VQE on Aer qasm simulator (with noise): {result1.eigenvalue.real:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can notice that, while the noiseless simulation's result is closer to the exact reference value, there is still some difference. This is due to the sampling noise, introduced by limiting the number of shots to 1024. A larger number of shots would decrease this sampling error and close the gap between these two values.\n",
    "\n",
    "As for the noise introduced by real devices (or simulated noise models), it could be tackled through a wide variety of error mitigation techniques. The [Qiskit Runtime Primitives](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/) have enabled error mitigation through the `resilience_level` option. This option is currently available for remote simulators and real backends accessed via the Runtime Primitives, you can consult [this tutorial](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/tutorials/Error-Suppression-and-Error-Mitigation.html) for further information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
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       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.22.2</td></tr><tr><td><code>qiskit-aer</code></td><td>0.11.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.7.1</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.19.2</td></tr><tr><td><code>qiskit</code></td><td>0.39.2</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.10.2</td></tr><tr><td>Python compiler</td><td>Clang 13.0.0 (clang-1300.0.29.30)</td></tr><tr><td>Python build</td><td>v3.10.2:a58ebcc701, Jan 13 2022 14:50:16</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>64.0</td></tr><tr><td colspan='2'>Fri Nov 18 01:03:00 2022 CET</td></tr></table>"
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       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2022.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
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       "<IPython.core.display.HTML object>"
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   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  }
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